It's future tense because someone wrote it that way, although I have to admit that the sentence is rather strange. But, imagine, that you are reading the beginning of "A Series of Unfortunate Events"...
The main verb is "zostaną", so "zostać" is the infinitive. Yes, it's perfective, because apparantly, they should be raised 'til the end' in this house, it's not just one of the places where they "będą wychowywani".
I guess "Oni są wychowywani w tym domu". "I guess" because this would better sound in past tense "They were raised in this house" "Oni byli wychowani w tym domu" or "Oni wychowali się w tym domu" (this sounds a little funny because it literally says "they raised themselves", but it really does mean "they were raised").
Both are equally plausible. Since this sentence features an omitted/implied third person subject pronoun, it is very likely that the subject was mentioned in the previous sentence.
If the previous sentence had 'dzieci' as a subject, then it would be 'wychowane'. If it was 'Tomek i Kasia', then it would be 'wychowani'.
Even if Tomek and Kasia are six-month-old twins? And if they aren't quite young, they can't be "raised" (or "brought up").
'Tomek' might be the name of a man or an adolescent (giving us 'wychowani'), but here it should be the name of a very young boy--and wouldn't that require 'wychowane'?
As alik explained before, if the subject is "dzieci", then it is "wychowywane", but Tomek i Kasia are "wychowywani" no matter how young they are.
And yes, Tomek is a name of a young boy, although he can be Tomek to his mom or his wife when he is 50. But for everybody else a man would rather be Tomasz.